Sub-Nyquist Sampling: Bridging Theory and Practice

Sampling theory encompasses all aspects related to the conversion of continuous-time signals to discrete streams of numbers. The famous Shannon-Nyquist theorem has become a landmark in the development of digital signal processing. In modern applications, an increasingly number of functions is being pushed forward to sophisticated software algorithms, leaving only those delicate finely-tuned tasks for the circuit level. In this paper, we review sampling strategies which target reduction of the ADC rate below Nyquist. Our survey covers classic works from the early 50's of the previous century through recent publications from the past several years. The prime focus is bridging theory and practice, that is to pinpoint the potential of sub-Nyquist strategies to emerge from the math to the hardware. In that spirit, we integrate contemporary theoretical viewpoints, which study signal modeling in a union of subspaces, together with a taste of practical aspects, namely how the avant-garde modalities boil down to concrete signal processing systems. Our hope is that this presentation style will attract the interest of both researchers and engineers in the hope of promoting the sub-Nyquist premise into practical applications, and encouraging further research into this exciting new frontier.Comment: 48 pages, 18 figures, to appear in IEEE Signal Processing Magazin

Estimation of Sparse MIMO Channels with Common Support

We consider the problem of estimating sparse communication channels in the MIMO context. In small to medium bandwidth communications, as in the current standards for OFDM and CDMA communication systems (with bandwidth up to 20 MHz), such channels are individually sparse and at the same time share a common support set. Since the underlying physical channels are inherently continuous-time, we propose a parametric sparse estimation technique based on finite rate of innovation (FRI) principles. Parametric estimation is especially relevant to MIMO communications as it allows for a robust estimation and concise description of the channels. The core of the algorithm is a generalization of conventional spectral estimation methods to multiple input signals with common support. We show the application of our technique for channel estimation in OFDM (uniformly/contiguous DFT pilots) and CDMA downlink (Walsh-Hadamard coded schemes). In the presence of additive white Gaussian noise, theoretical lower bounds on the estimation of SCS channel parameters in Rayleigh fading conditions are derived. Finally, an analytical spatial channel model is derived, and simulations on this model in the OFDM setting show the symbol error rate (SER) is reduced by a factor 2 (0 dB of SNR) to 5 (high SNR) compared to standard non-parametric methods - e.g. lowpass interpolation.Comment: 12 pages / 7 figures. Submitted to IEEE Transactions on Communicatio

Communications techniques and equipment: A compilation

This Compilation is devoted to equipment and techniques in the field of communications. It contains three sections. One section is on telemetry, including articles on radar and antennas. The second section describes techniques and equipment for coding and handling data. The third and final section includes descriptions of amplifiers, receivers, and other communications subsystems

Coherent terabit communications with microresonator Kerr frequency combs

Optical frequency combs enable coherent data transmission on hundreds of wavelength channels and have the potential to revolutionize terabit communications. Generation of Kerr combs in nonlinear integrated microcavities represents a particularly promising option enabling line spacings of tens of GHz, compliant with wavelength-division multiplexing (WDM) grids. However, Kerr combs may exhibit strong phase noise and multiplet spectral lines, and this has made high-speed data transmission impossible up to now. Recent work has shown that systematic adjustment of pump conditions enables low phase-noise Kerr combs with singlet spectral lines. Here we demonstrate that Kerr combs are suited for coherent data transmission with advanced modulation formats that pose stringent requirements on the spectral purity of the optical source. In a first experiment, we encode a data stream of 392 Gbit/s on subsequent lines of a Kerr comb using quadrature phase shift keying (QPSK) and 16-state quadrature amplitude modulation (16QAM). A second experiment shows feedback-stabilization of a Kerr comb and transmission of a 1.44 Tbit/s data stream over a distance of up to 300 km. The results demonstrate that Kerr combs can meet the highly demanding requirements of multi-terabit/s coherent communications and thus offer a solution towards chip-scale terabit/s transceivers

Linearization techniques to suppress optical nonlinearity

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis is shown the implementation of the linearization techniques such as feedforward and pre-distortion feedback linearization to suppress the optical components nonlinearities caused by the fibre and semiconductor optical amplifier (SOA). The simulation verified these two linearization techniques for single tone direct modulation, two tone indirect modulation and ultra wideband input to the optical fibre. These techniques uses the amplified spontaneously emission (ASE) noise reduction in two loops of SOA by a feed-forward and predistortion linearizer and is shown more than 6dB improvement. Also it investigates linearization for the SOA amplifier to cancel out the third order harmonics or inter-modulation distortion (IMD) or four waves mixing. In this project, more than 20 dB reductions is seen in the spectral re-growth caused by the SOA. Amplifier non-linearity becomes more severe with two strong input channels leading to inter-channel distortion which can completely mask a third adjacent channel. The simulations detailed above were performed utilizing optimum settings for the variable gain, phase and delay components in the error correction loop of the feed forward and Predistortion systems and hence represent the ideal situation of a perfect feed-forward and Predistortion system. Therefore it should be consider that complexity of circuit will increase due to amplitude, phase and delay mismatches in practical design. Also it has describe the compatibility of Software Defined Radio with Hybrid Fibre Radio with simulation model of wired optical networks to be used for future research investigation, based on the star and ring topologies for different modulation schemes, and providing the performance for these configurations

The development of speech coding and the first standard coder for public mobile telephony

This thesis describes in its core chapter (Chapter 4) the original algorithmic and design features of the ??rst coder for public mobile telephony, the GSM full-rate speech coder, as standardized in 1988. It has never been described in so much detail as presented here. The coder is put in a historical perspective by two preceding chapters on the history of speech production models and the development of speech coding techniques until the mid 1980s, respectively. In the epilogue a brief review is given of later developments in speech coding. The introductory Chapter 1 starts with some preliminaries. It is de- ??ned what speech coding is and the reader is introduced to speech coding standards and the standardization institutes which set them. Then, the attributes of a speech coder playing a role in standardization are explained. Subsequently, several applications of speech coders - including mobile telephony - will be discussed and the state of the art in speech coding will be illustrated on the basis of some worldwide recognized standards. Chapter 2 starts with a summary of the features of speech signals and their source, the human speech organ. Then, historical models of speech production which form the basis of di??erent kinds of modern speech coders are discussed. Starting with a review of ancient mechanical models, we will arrive at the electrical source-??lter model of the 1930s. Subsequently, the acoustic-tube models as they arose in the 1950s and 1960s are discussed. Finally the 1970s are reviewed which brought the discrete-time ??lter model on the basis of linear prediction. In a unique way the logical sequencing of these models is exposed, and the links are discussed. Whereas the historical models are discussed in a narrative style, the acoustic tube models and the linear prediction tech nique as applied to speech, are subject to more mathematical analysis in order to create a sound basis for the treatise of Chapter 4. This trend continues in Chapter 3, whenever instrumental in completing that basis. In Chapter 3 the reader is taken by the hand on a guided tour through time during which successive speech coding methods pass in review. In an original way special attention is paid to the evolutionary aspect. Speci??cally, for each newly proposed method it is discussed what it added to the known techniques of the time. After presenting the relevant predecessors starting with Pulse Code Modulation (PCM) and the early vocoders of the 1930s, we will arrive at Residual-Excited Linear Predictive (RELP) coders, Analysis-by-Synthesis systems and Regular- Pulse Excitation in 1984. The latter forms the basis of the GSM full-rate coder. In Chapter 4, which constitutes the core of this thesis, explicit forms of Multi-Pulse Excited (MPE) and Regular-Pulse Excited (RPE) analysis-by-synthesis coding systems are developed. Starting from current pulse-amplitude computation methods in 1984, which included solving sets of equations (typically of order 10-16) two hundred times a second, several explicit-form designs are considered by which solving sets of equations in real time is avoided. Then, the design of a speci??c explicitform RPE coder and an associated eÆcient architecture are described. The explicit forms and the resulting architectural features have never been published in so much detail as presented here. Implementation of such a codec enabled real-time operation on a state-of-the-art singlechip digital signal processor of the time. This coder, at a bit rate of 13 kbit/s, has been selected as the Full-Rate GSM standard in 1988. Its performance is recapitulated. Chapter 5 is an epilogue brie y reviewing the major developments in speech coding technology after 1988. Many speech coding standards have been set, for mobile telephony as well as for other applications, since then. The chapter is concluded by an outlook